Help for McLaren's two papers

Hello ALL, I am working on deriving thaat-s (sca;es) in Indian music (both =
Hindustani and Karnatic genres). While we come across numbers like 32 and 72=
, I am looking for something more fundamental.

Can you help me get copies of the following --

# McLaren, Brian. "General Methods of Generating Musical Scales", Xenharmon=
ikôn vol. 13, 1990.
McLaren, Brian. "Macrotonal Scales", Xenharmonikôn vol. 16, autumn 1995, p.=
36.

thanking you, and highly appreciative of any help offered,
Haresh.

>Can you help me get copies of the following --
>
># McLaren, Brian. "General Methods of Generating Musical Scales",
>Xenharmonikôn vol. 13, 1990.
>
>McLaren, Brian. "Macrotonal Scales", Xenharmonikôn vol. 16,
>autumn 1995, p. 36.
>
>thanking you, and highly appreciative of any help offered,
>Haresh.

Back issues of Xenharmonikon are available from Frog Peak music...

http://www.frogpeak.org/fpartists/fpchalmers.html

-Carl

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> Hello ALL, I am working on deriving thaat-s (sca;es) in Indian
music (both =
> Hindustani and Karnatic genres).

hindustani music uses 10 thaats, correct?

> While we come across numbers like 32 and 72=
> , I am looking for something more fundamental.
>
> Can you help me get copies of the following --
>
> # McLaren, Brian. "General Methods of Generating Musical Scales",
Xenharmon=
> ikôn vol. 13, 1990.
> McLaren, Brian. "Macrotonal Scales", Xenharmonikôn vol. 16, autumn
1995, p.=
> 36.
>
> thanking you, and highly appreciative of any help offered,
> Haresh.

hi haresh, i'd love to help. what is it that you think would be
helpful in the papers above?

please tell me what you have in mind when you say "fundamental". do
you mean at the level of shrutis rather than at the level of
semitones? then you're likely to have even more than 10, 32, or
72 . . . or would you like to restrict this in some way?

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
> wrote:
,,,,,,,,,,,,,,,,,,

> > Can you help me get copies of the following --
> >
> > # McLaren, Brian. "General Methods of Generating Musical Scales",
> Xenharmon=
> > ikôn vol. 13, 1990.
> > McLaren, Brian. "Macrotonal Scales", Xenharmonikôn vol. 16, autumn
> 1995, p. 36.
...............
> hi haresh, i'd love to help. what is it that you think would be
> helpful in the papers above?
>
> please tell me what you have in mind when you say "fundamental". do
> you mean at the level of shrutis rather than at the level of
> semitones? then you're likely to have even more than 10, 32, or
> 72 . . . or would you like to restrict this in some way? >>>>>>>>

Hello Paul, that is one of the blocks: I, simply, do not know. But let me m=
ake my confusion clear: On the one hand, we have the 72-note melakarta syste=
m in Karnatic music. Those 72 scales are raga-s, too -- they can be elaborat=
ed. On the other hand, we have Bhatkhande's 10-thaat classification to work =
as the raga generators. But these 10 thaat-s are NOT raga-s -- they cannot b=
e performed. And then we have the raganga paddhati (system). The latter clas=
sifies raga-s in terms of some fundamental structures. This classification i=
s not scales at all; they are actual raga-s to be performed. I am looking fo=
r scales only.

Now, using the 12-note Indian gamut, we can derive 32 scales -- and ONLY 32=
. They are scales, not raga-s. Let me show that, though this is very obvious=
:

The 16 (of the 32) thaat-s, using F (and not F#):
-------------------------------------------------

1. C D E F
2. C Db E F
3. C D Fb F
4. C Db Eb F

Each of the above combines with each of the following:

1. G A B c
2. G Ab B c
3. G A Bb c
4. G Ab Bb c

This gives 16 thaat-s. Now, by substituting F above with F#, we get other 1=
6 -- a total of 32. [This better than the Bhatkhande system, because it acco=
mmodates several more raga-s than the former system.]

The query: There is nothing fundamental about this. What are the fundamenta=
ls of scale formation, anyway? Are they mentioned in McLaren's papers? Or, i=
n John Chalmer's book on tetrachords?

Thanking you for your time, and regards,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:

> The query: There is nothing fundamental about this. What are the
>fundamenta=
> ls of scale formation, anyway?
> Are they mentioned in McLaren's
>papers?

mclaren essentially considers any novel set of pitches (typically he
used complex but arbitrary mathematical formulae to generate them) to
be valid as a scale. here in boston, the local microtonal society is
also concerned with novelty as opposed to following any rules or
fundamentals, but the approach is hardly ever mathematical at all,
and even scales themselves can be a rarity (other than their 72-equal
master pitch set).

> Or, i=
> n John Chalmer's book on tetrachords?

you'll find a host of historical and theoretical constructs there,
but again little prescription as to what is "fundamental".

> Thanking you for your time, and regards,
> Haresh.

haresh, one of the subjects i have spent a great deal of time on is
the subject of periodicity blocks, which as a fundamental principle
of scale construction has much, if not everything, in common with
the "constant structure" criteria for valid scales that kraig grady
has appealed to, referring to erv wilson's work. please take some
time to read or reread my "gentle introduction to fokker periodicity
blocks", which starts here:

http://sonic-arts.org/td/erlich/intropblock1.htm

after you are done i'll have you look at my "forms of tonality",
which thanks to carl (and no thanks to my typos) is now on the
web . . .

some of erv wilson's work, approaching which is often like solving a
crossword puzzle before you can begin to see what he's saying (well
worth the effort), can be found here:

http://www.anaphoria.com/wilson.html

please come back with as many questions as you need answered!

good luck,
paul

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Can you help me get copies of the following --
....
>
> Back issues of Xenharmonikon are available from Frog Peak music...
>
> http://www.frogpeak.org/fpartists/fpchalmers.html
>
> -Carl

Thanks, Carl. Haresh.

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
....

Thanks Paul. I will work on the details you have given. Haresh.

hello all,

just letting everyone know that i've been
having mysterious email problems ever since
the big virus that went around a few weeks ago.

stopping email from Yahoo groups seems to get
rid of the problem, but when i turn email from
Yahoo groups back on again, it returns. i can't
tell if it's a problem with my own system (which
seems to be entirely clean and virus-free) or
with my server.

anyway, i have mostly *not* been receiving Yahoo
group postings in my email inbox lately, and
only reading message on the Yahoo interface now
and then. so if someone is trying to reach me
you should email me directly.

-monz

hello all,

regarding the database:

5-limit commas and their associated linear temperaments

/tuning/database?method=reportRows&tbl=10

can we come up with names for the commas that still
don't have names?

-monz

>can we come up with names for the commas that still
>don't have names?

Again, a tuning-math question. But I'd rather we didn't.
The names are cute but getting out of hand. Write a
piece of music, get a name; maybe that should be the
general rule.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Again, a tuning-math question. But I'd rather we didn't.
> The names are cute but getting out of hand. Write a
> piece of music, get a name; maybe that should be the
> general rule.

Heh. Can you really envision someone writing a piece in the atom
temperament?

--- In tuning@yahoogroups.com, <monz@a...> wrote:
> hello all,
>
>
> regarding the database:
>
> 5-limit commas and their associated linear temperaments
>
> /tuning/database?
method=reportRows&tbl=10
>
>
>
> can we come up with names for the commas that still
> don't have names?
>
>
>
>
> -monz

right now on the _small 5-limit intervals_ "honeycomb" chart on your
equal temperament page,

http://sonic-arts.org/dict/eqtemp.htm

we have "(amity)", "(negri)", and "(semisixths)" for the unison
vectors (1600000:1594323, 16875:16384, and 78732:78125, respectively)
that vanish in the amity, negri, and semisixths temperaments
respectively. the precedent is "schismic" and "schismatic" to
describe temperaments where the schisma vanishes, not sure if graham
breed was the first to do this or if it was done before. you could
follow this model for all the unnamed unison vectors in the table
above, if you wish. the only confusion is that the pythagorean comma
does not vanish in pythagorean tuning, so would be sort of an
exception to this pattern.

Paul Erlich wrote:

>we have "(amity)", "(negri)", and "(semisixths)" for the unison >vectors (1600000:1594323, 16875:16384, and 78732:78125, respectively) >that vanish in the amity, negri, and semisixths temperaments >respectively. the precedent is "schismic" and "schismatic" to >describe temperaments where the schisma vanishes, not sure if graham >breed was the first to do this or if it was done before. you could >follow this model for all the unnamed unison vectors in the table >above, if you wish. the only confusion is that the pythagorean comma >does not vanish in pythagorean tuning, so would be sort of an >exception to this pattern.
> >
The original term is "schismatische Verwechslung" which I think was either Helmholtz or Riemann(?). It's covered in Liberty Manik's treatise on Arabic theory, anwyay, which I never completely understood. Ellis translated it as "skhismatic" but there are all kinds of variants ;-) It's the same Greek root as "schism".

Graham

hi Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >can we come up with names for the commas that still
> >don't have names?
>
> Again, a tuning-math question.

why is that?

> But I'd rather we didn't.
> The names are cute but getting out of hand. Write a
> piece of music, get a name; maybe that should be the
> general rule.

i'm using a list of intervals in my software, and it
would be nice if they all had names. otherwise, some
will just have to be called "<n/a>", which can stand
for either "not available" or "not applicable" as you like.

-monz

>> >can we come up with names for the commas that still
>> >don't have names?
>>
>> Again, a tuning-math question.
>
>
>why is that?

Because that's where lists of commas are usually posted around
here, and where people usually go to become immortalized through
nomenclature.

>> But I'd rather we didn't.
>> The names are cute but getting out of hand. Write a
>> piece of music, get a name; maybe that should be the
>> general rule.
>
>
>i'm using a list of intervals in my software, and it
>would be nice if they all had names. otherwise, some
>will just have to be called "<n/a>", which can stand
>for either "not available" or "not applicable" as you like.

Why not call them by their ratio (or in prime factor notation
if too big)?

-Carl

In the following, I will write "komma" for the more general term and "comma" for the restricted size range.

During the development of the sagittal notation system, George and I looked at a _lot_ of kommas, and eventually came up with a descriptive naming system that worked for us, in the sense that it
(a) is consistent with most existing names,
(b) automatically gives _unique_ names to hundreds of the most commonly encountered notational kommas,
(c) gives _short_ names to hundreds of the most commonly encountered notational kommas,
(d) gives names that make it possible to unpack the komma ratio from the name, if the naming-system is known, (and maybe even if it isn't).

The latter property is very valuable and is something that naming after people, or pieces of music, can never give.

This system won't necessarily suit the temperament-cataloging project, but it can probably be adapted.

The kommas we examined were generated by starting with a list of all the ratios that appear in the Scala archive, along with counts of their number of ocurrences (courtesy of Manuel Op de Coul).

The factors of 2 and 3 were removed from these ratios, then like ratios had their ocurrences combined and they were sorted by number of ocurrences (popularity). Then for each 2,3-reduced ratio we found all the kommas having an absolute 3-exponent not greater than 12 and a size not greater than 70 cents. I imagine these ranges would need to be increased for the temperament project. There was another constraint on komma "slope" which I won't go into here as it probably isn't relevant to your purposes.

The first part of the komma name is simply the two sides of the 2,3-reduced ratio, with a colon between. As a convention, we put the smallest number first. If one side of the reduced ratio is unity, we omit it, and the colon. When speaking, the colon is not pronounced. And you are welcome to pronounce 1 (which is equivalent to 3 in this system) as "Pythagorean", 5 as "classic", 7 as "septimal", 11 as "undecimal", etc., but I find it's easier just to say them in English.

The second part of the name is one of

schismina
schisma
kleisma
comma
small diesis
(medium) diesis
large diesis

This part of the name is made to do double duty. It not only gives the size category, but it distinguishes multiple kommas for the same 2,3-reduced ratio. To do this, the boundaries between categories have to be chosen very carefully. An intial set of category names and approximate boundaries were obtained by looking at the existing komma names in Scala's intnam.par.

Then we worked our way down the ratio popularity list, and whenever we found two kommas for the same ratio in the same category, we moved an existing boundary if we could do so without upsetting any previous ratios, or otherwise added a new boundary and category.

We didn't bother moving a boundary to separate two commas for the same ratio when they were less than about 0.7 c apart, but I imagine you would need to do this for your purposes. We also made boundary decisions based on the boundaries between sagittal symbols which would not be relevant. So you might repeat this process with larger 3-exponents etc., and come up with slightly different boundaries and more size categories. Some of the boundaries we obtained are very similar to some obtained by Monz in
http://sonic-arts.org/td/monzo/o483-26new5limitnames.htm

Here's what we are using (cents)
0
schismina
0.98
schisma
4.5
kleisma
13.47
comma
36.93
small diesis
45.11
(medium) diesis
56.84
large diesis
68.57

Some of these are very precisely defined as they are exact square-roots of 3-limit kommas. The boundaries seem to naturally want to fall on these. 56.84 is actually a half apotome. 45.11 is actually a half Pythagorean limma. The kleisma/comma boundary really wants to be half the Pythagorean comma and the comma/small-diesis boundary seems to want to be about 33.38 cents, which looks like half the [27,-17] comma. The medium/large diesis boundary is at half of [-30,19].

Maybe the next higher boundary (large diesis/small semitone?) should be at 78.49 c, half of [35,-22]. The schismina/schisma and schisma/kleisma boundaries were not actually needed (by us) to distinguish same-ratio kommas, and so are somewhat arbitrary, but maybe they can usefully be assigned roots of other 3-limit commas.

And by the way, I think that, in general, new or obscure temperaments are more usefully named after their generators, than their vanishing commas.
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com/

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >can we come up with names for the commas that still
> >> >don't have names?
> >>
> >> Again, a tuning-math question.
> >
> >
> >why is that?
>
> Because that's where lists of commas are usually posted around
> here, and where people usually go to become immortalized through
> nomenclature.

but since when is something as basic to tuning as
names of intervals too technical for this list?

i can understand using the tuning-math forum for
something that really does get deeply into the math,
but come on, this is tuning kindergarten stuff.

anyway ... i see that Dave Keenan has apologetically
posted the most substantial response to this thread on
that list, so i pursue if further over there.

-monz

Sorry, but I'm trying to sign off the list... but I can´t get it. Any ideas?
Thanks in advance.

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Cristina Portillo

E-mail: xtina@platea.pntic.mec.es